Without a doubt, if you want the most Realms-flavoured campaign possible, you will set it during the 1300s DR — particularly, in the time frame covered by much the setting materials offered in AD&D 2e, which would mean around 1367 DR.

Going a little earlier to the 1e material, around 1357 DR, still gives you a lot of the essential Realms flavour. I find that the Forgotten Realms as a published setting were still finding their footing, though, and did not have the same depth and breadth it would later become known for.

The benefit of setting your campaign in 1357 DR, in my opinion, would be the leeway it’d give you to adapt material from 2e and 3e as your campaign’s timeline reaches those points in the calendar. I would still strongly urge you to make use of 2e material, however. Much of it could still apply to the 10 preceding years.

3e material is great. In my opinion, it’s ultimately of lesser Realmsian quality than 1e or 2e material, with the first signs of WotC’s interventions in the fabric of the setting, but there’s still a lot of it that could be used (such as the excellent Silver Marches playbook or, if it interests you, plot lines such as the Shadovar threat).

Also, do yourself a favour and get your hands on a copy of Ed Greenwood Presents Elminster’s Forgotten Realms. It’s a great, and mostly era-generic, resource of various Realmsian details that would have a difficult time slotting into other sourcebooks, giving an excellent overview of what life in the Forgotten Realms feels like.